Calculate the standard deviation of the data set below. (7, 9, 10, 11, 13)

The standard deviation of the data set is:

                      2

We are given a set of data points as:

x=  7   9   10    11    13

Now on firstly finding the mean of these data points we have:

Now,

 x             x-x'             (x-x')²

 7           7-10=-3           9

 9           9-10=-1            1

10          10-10=0           0

11            11-10=1             1

13           13-10=3           9      

∑(x-x')²=20

Now, mean of  ∑(x-x')² gives us the variance of the data.

Variance=∑(x-x')²/5=20/5=4

Now, we know that standard deviation is the square root of variance.

Hence,

Standard deviation=√4=2